In my experience of driving auto 4x4s in alpine areas the auto should be driven like a manual, making use of the '3-2-L or 2-L' gear stick position options. By design, and our preference, the autos in our simple vehicles can't tell that its climbing a steep mountain pass so it will keep changing gears as normal, whereas modern vehicles with tons of sensors that all talk to each other would probably be analysing the outside temp and altitude amongst other data to inform the auto gearbox that it needs to adapt its shift pattern accordingly. So in our simpler vehicles we need to do that for the auto gearbox, to protect it and help it get to the top without overheating the ATF.
By selecting one of the '3-2-L' positions you are limiting the gearbox to that gear as its highest gear, then it will hold that gear and you can use the engine revs more, without the risk of the box changing up (it will only override this if you push the gearbox too hard and risk damage). This is a really useful option as a large amount of heat is generated when an auto changes gear.
Putting things into context, a 4x4 is a heavy vehicle which tends to be even heavier when loaded for a trip, we tend to prefer holidaying when the weather is nice so theres a good chance that the ambient temperature is high, mountains tend to be high and steep with loads of switchbacks to allow a vehicle to scale it, and the higher you go the thinner the air gets. So you end up with a heavily laden vehicle scaling switchback after switchback at slow speed, with high ambient temperatures and thin air. The thin air will make the turbo charged diesel engines that often power 4x4s become less efficient and therefore work harder, couple this with the slow speed and therefore reduced airflow over the cooling radiators and its easy to see how this situation can exploit any weakness in vehicle, or push a perfectly functional vehicle outside of its safe operating parameters.
In my experience its easy to overheat an auto in these conditions if it is just left in D and has to work out when to change gear for itself. As the 4x4 is slowly ascending the short stretches between the switchbacks that auto spends a longtime waiting for the engine and road speeds to be appropriate to select the next gear up, then it will change up and start the whole process again to select the next gear. This process generates a lot of heat for every gear change, this heat has to be dissipated by the auto gearbox cooler, be it in the engine radiator or a separate cooler. If it is in the engine radiator then bear in mind that the engine so also working hard and is trying shed a load of heat through its coolant at the same time, which could have an impact on the auto coolers ability to exchange the heat with the coolant. UK market diesel 80's have the auto cooler built into the bottom of the engine rad, but in my experience it is well up to the task of cooling the auto gearbox if the temperatures are managed.
So with the gear changes generating the heat as the 4x4 ascends the mountain, the key is to try and keep them to a minimum and avoid unnecessary changes. I drive my auto like a manual in these conditions and only shift gear if its beneficial, if the length between the switch back is just so that really the 4x4 could pull 3rd but it would only be for a short distance until the next switchback, then I tend to leave it in 2nd and use the engine revs a bit more, or just manage my speed accordingly and not try to race up the mountain, after all the key is vehicle preservation when you are far from home.
Coming into a switchback I would shift down to the appropriate gear for the exit of the switchback onto the next climb, as if you leave the gearstick in 3rd or 2nd the 4x4 will try and hold this gear and then change down once it decides it can't pull the load up the gradient in the current gear, this also generates a lot of heat in the auto gearbox. So by reading the road and shifting the gears accordingly you can be in the right gear to get back on the power as you exit the switchback and make best use of the engines revs and the 4x4s momentum. If the switchback isn't too sharp it may be possible to hold 2nd and keep some of the vehicles momentum as you corner and power out, this obviously avoids generating additional heat by working through 1st and back into 2nd if it wasn't necessary.
By manually selecting the gears in this way you can keep on top of the heat generated inside the auto box within levels that aren't damaging to the ATF or auto gearbox and can be managed by the auto gearbox cooler. Employing this method has allowed me to ascend many alpine routes without the need to stop and allow the gearbox to cool as the overheat warning light has illuminated. That being said it is a very fine line and is specific to the vehicles condition, load and modifications, all of which have a bearing on the auto gearboxes ability to generate and dissipate heat.
Obviously any Overdrives want to be in the OFF position when ascending mountains, and if your auto has a 'sports mode' or ECT (electronic control transmission) as seen on post 1992 80's, this can be used to hold the gears longer if you decide you need a break from manually selecting the gears or want to leave the gearstick in 2nd or 3rd and allow the auto to do the shifting up to those gears.
Measures can be taken to assist with the preservation of the auto gearbox, as have been suggested in this thread, such as an ATF temperature gauge/additional ATF cooler/manual lock up devices. I haven't gone down this route (yet), instead I have chosen to make sure that my cooling system and auto gearbox cooling systems are tip top and then put my faith in them as the designers did an awful lot of hot weather testing on these systems and deemed them capable. Sometimes aftermarket kit can give trouble if they are poorly thought out or installed, after all the OEM set up has lasted 20+ years on many of the 4x4s that people use for overlanding, yet you find that an aftermarket cooler or gauge starts give trouble due to a poor connection or rubbed through hose after just a couple of years. So first make sure the OEM set up is tip top, then choose aftermarket modifications carefully and make sure that they are correctly installed and fit for the environment that the 4x4 is going to operate in, as what may last years running around in the UK may fail after just one Morocco trip.
What goes up........must come down! I find ascending easier than descending, as you can easily stop during an ascent to have a breather, but during a decent if you haven't been preserving the brakes it can be very difficult to stop an auto.
As a general rule autos provide less engine braking than a manual, so descending a mountain in a heavily laden auto 4x4 is a game of making the best of the engine braking available by manually shifting the auto gearbox and careful use of the brakes. I have had to stop on a couple of occasions to allow the brakes to cool during a descent as the early on set of brake fade could be detected. I find high boiling point brake fluid and uprated brakes can help. Just leaving the gear stick in D and leaving all the braking to the brakes can result in total brake failure, I have seen it happen, so much smoke was pouring off of all four brake discs that people thought the 4x4 was on fire and came running with fire extinguishers, (no this wasn't my vehicle).
I hope that is some help and if it saves one persons auto gearbox it was worth the effort in typing!
Pumpy - Sorry this has come post your trip but I hope that some of it may help you on the next one. As has been advised elsewhere, I would change your ATF even though it seems ok, as it has seen some action which has probably shortened its useful life expectancy. plus it has already done its job.